Bi-objective optimization of biclustering with binary data

• Published in: Information sciences 2020-10, Vol.538, p.444-466
• Main Authors: Hanafi, Saïd, Palubeckis, Gintaras, Glover, Fred
• Format: Article
• Language: English
• Subjects: Bi-clustering; Bi-objective optimization; Biclique; Computer Science; ε-Constraint method
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2020.05.078

•A bi-objective optimization approach is introduced for biclustering with binary data.•Integer programming formulations are provided for bi-objective biclustering.•We propose and implement an efficient heuristic based on set intersection operations.•Experimental testing yields very good results and significantly reduced CPU time. Clustering consists of partitioning data objects into subsets called clusters according to some similarity criteria. This paper addresses a structure for generating overlapping clusters, where data objects can belong to more than one subset, which we join with bi-objective optimization and link to biclustering for problems with binary data. Biclustering simultaneously groups the objects and features so that a specific group of objects has a special group of features. In recent years, biclustering has received a lot of attention in several practical applications. First we present an integer programing formulations for the bi-objective optimization of biclustering. Next we propose a constructive heuristic based on the set intersection operation and its efficient implementation for solving a series of mono-objective problems used inside the ε-constraint method (obtained by keeping only one objective function and the other objective function is integrated into constraints). Finally, our experimental results show that our proposed heuristic provides very good results and significantly reduces the computational expense compared to using the CPLEX solver as an exact algorithm for finding an optimal solution, which drastically increases the computational cost for large instances.